The binary value for 255 is 11111111, with all of the memory locations used up. How can greater numbers, for example, 481 be denoted? Will they be written singularly, like (considering the above example), 00110100 00111000 00110001?
It depends on the number of bits you use. In your example, you've used an 8 bit (one byte) number, which does max out at 255.
Ever since forever, computers have used numbers that are larger than one byte.
For example, in Fortran (invented in 1977) 'real' numbers use 4 bytes, and can store numbers up to 11111111 11111111 11111111 11111111 = 2,147,483,647
For when that isn't enough, Fortran includes the 'double precision' numbers which use 8 bytes.